Datta Abhirup, Banerjee Sudipto, Hodges James S, Gao Leiwen
Johns Hopkins University.
University of California Los Angeles.
Bayesian Anal. 2019 Dec;14(4):1221-1244. doi: 10.1214/19-ba1177. Epub 2019 Oct 3.
Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used ICAR model, which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on a directed acyclic graph (DAG) representation of the spatial dependence. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated random effects, can also directly model the outcome from dependent data like images and networks. Theoretical results establish a link between the parameters in our model and the variance and covariances of the random effects. Substantive simulation studies demonstrate that the improved interpretability of our model reaps benefits in terms of accurately recovering the latent spatial random effects as well as for inference on the spatial covariance parameters. Under modest spatial correlation, our model far outperforms the CAR models, while the performances are similar when the spatial correlation is strong. We also assess sensitivity to the choice of the ordering in the DAG construction using theoretical and empirical results which testify to the robustness of our model. We also present a large-scale public health application demonstrating the competitive performance of the model.
用于区域汇总疾病发病率数据的分层模型通常涉及特定区域的潜在随机效应，这些效应被联合建模为具有多元高斯分布。协方差矩阵或精度矩阵纳入了区域之间的空间依赖性。精度矩阵的常见选择包括广泛使用的ICAR模型（它是奇异的）及其缺乏可解释性的非奇异扩展。我们基于空间依赖性的有向无环图（DAG）表示，为精度矩阵提出了一种新的参数模型。我们的模型保证正定，因此，除了作为区域空间相关随机效应的有效先验之外，还可以直接对来自图像和网络等相关数据的结果进行建模。理论结果建立了我们模型中的参数与随机效应的方差和协方差之间的联系。大量的模拟研究表明，我们模型的可解释性提高在准确恢复潜在空间随机效应以及对空间协方差参数进行推断方面都带来了好处。在适度的空间相关性下，我们的模型远远优于CAR模型，而在空间相关性较强时，性能相似。我们还使用理论和实证结果评估了DAG构建中排序选择的敏感性，这些结果证明了我们模型的稳健性。我们还展示了一个大规模的公共卫生应用，证明了该模型的竞争性能。
